University of Virginia
Physics Department

## The Frequency of Sound

A Physical Science Activity

2003 Virginia SOLs

• PS.1
• PS.8

Objectives

Students will

• learn the relationship between sound and vibration waves in air;
• experimentally determine the frequency of a sound source;
• learn the relationship between the frequency and the period of waves;
• learn that high frequency waves produce higher pitched sounds and lower frequency produces lower pitches;
• learn about the Doppler Effect.

Motivation for Learning

Demonstration: The magic metal

Materials:
• Tuning fork
• One 2-m long, strong string
• Electrical tape

Procedure

• Attach the string to the handle of a tuning fork by wrapping several turns of string around the handle, tying a knot around it and also wrapping the handle with electrical tape. It is recommended to use a saddle-type knot as shown. Caution: make sure the string is strongly attached by trying to yank it off. If it moves at all, make it tighter.

• Go to the middle of the room and have the students stand at one end of the room.
• Hit the tuning fork so that you can hear the pitch. Then while holding the string at the other end, start spinning the tuning fork around.
• Ask the students to decide on which side of the spinning circle they hear a higher pitch and a lower pitch. Take a vote by having them shout high or low. The side where the tuning fork is going towards them should get the most if not all "highs" and the other side "lows".
• Now split the students so that half are in the back and half are in the front of class. Perform the same spinning, then take another vote. Is the result the same?

Background Information

Sound waves consist of a series of air pressure variations. When the tuning fork is hit, the metal rods oscillate (similar to how a car antenna goes back and forth when it is plucked). Air molecules are pushed around the fork, pushing other air molecules. As the fork continues to vibrate, it sends waves of sound through the air a lot like the ripples you see when a rock is dropped into a pond. Sound is heard when the rippling air pushes on our ear drum. Nerves in the ear canal send a message to the brain, which interprets these vibrations into sound impulses.

Why does the sound pitch get higher or lower when the fork is spun? Low-pitched sounds have big gaps between waves, while high-pitched sounds have waves that are emitted more closely together. When the fork is moving towards an observer, the waves bunch together, creating a higher frequency sound. When the fork moves toward the observer, the waves spread out, resulting in a lower frequency sound. When the class was split in the front and back of the room, everyone heard a pitch that was high or low, depending on the motion of the fork relative to the observers. This is called the Doppler Effect.

The time for one complete cycle of repetition (or one vibration) is called the period. Since it is a time measurement, we call it T. The reciprocal is the frequency f, or the number of complete cycles per second. 1 cycle per second is one Hertz or Hz. In this lab we will practice measuring the frequency of two different tuning forks.

### Student Activity

Materials

• Two tuning forks, preferably 30 - 70 Hz difference.
• CBL system
• TI-83 with PHYSICS software package
• Vernier microphone

Procedure

1. Connect the Vernier microphone to the CH1 input on the CBL. Use the black link cable to connect the CBL unit to the calculator. Firmly press in the cable ends.
2. Turn on the calculator and the CBL unit. Start the PHYSICS program and use the microphone setup for 1 probe (for info on how to download the PHYSICS programs go to http://www.vernier.com).
3. Choose the Waveform collection mode.
4. Choose one of your tuning forks and hit on a surface (not a hard surface, but something like the bottom of your shoe) SOFTLY to get it ringing. Note: the tuning forks do not need to be hit too hard, just enough to hear a solid tone.
5. Place the fork ends (without touching anything) near the microphone and start recording.
6. After the graph is displayed, record the y value for one of the peaks and then one of the troughs. (You only have to do this for one of them because they should all be about the same height. If the graph does not show sharp peaks and troughs, retake data.)
7. Calculate the total change in amplitude by adding the peak and trough amplitude values and dividing by 2. Be sure to make all of the values positive before adding.
8. Next find out how much time it took to go a given amount of cycles. One cycle is the amount of time it takes to go from one peak to the next, so put the cursor on one of the first peaks and mark down the time (the x value), then move the cursor over to one of the last peaks and measure the time. Every time you go from a peak to the next peak, that's a cycle! Count all the cycles between peaks and mark this number down on the Data Sheet.
9. In order to find out the time for just one cycle, divide the time it took for all of the cycles by the number of cycles you passed over. This is the period T.
10. Take 1/T to find the frequency.
11. Now, using the same fork, hit it harder to perform the same analysis as in steps 5-10
12. Perform the steps 5-10 for a soft hit and a hard hit of the other tuning fork.
13. Now select the Frequency collection mode from the program main menu. This feature measures the frequency for you! See if it does a good job by measuring the frequency for the loud and soft hits for both tuning forks and comparing them to your calculation of the frequency.

Data Sheet

 Fork # 1 1 2 2 Type of hit Soft Hard Soft Hard A Peak amplitude (V) B Trough amplitude (V) C Total amplitude (V) {(A+B)/2} D Initial time (s) E Final time (s) F Time interval (s) {E-D} G # of Cycles between times H Period (s) {F/G} I Frequency (Hz) {1/H} J Calculator Frequency (Hz)

Questions:

1. Does it matter how hard you hit the fork? Does the frequency change when you hit it harder? How about the amplitude?
2. Which tuning fork has a higher tone? How does the frequency of the high tone tuning fork compare with the frequency of the lower tone tuning fork?
3. To obtain the period and frequency, we measured the time over a lot of cycles, then divided. Why didn't we just measure the time over one cycle?
4. The frequency of the tuning fork is probably written on the handle. How well does your calculated value compare with this frequency?

Students with Special Needs

All students should be able to participate in this activity.

Click here for further information on laboratories with students with special needs.

Assessment

Data sheet and questions to be completed during laboratory.